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Max Tegmark admits that when asked about his field of study on a long airplane ride, he says one of two things. He will answer "Astronomy" if he wants to engage in conversation with his fellow passenger, but "Physics" if want to be left alone.

As a well-known cosmologist, Mr. Tegmark seems amused given that modern astronomy and physics are closely related with mathematics at the heart of both. In his new book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality," Mr. Tegmark argues that it is advances in mathematics that will provide the ultimate answers to nature of reality.

"Our Mathematical Universe" is a delightful book in which the Swedish-born author, now at MIT, takes readers on a roller coaster ride through cosmology, quantum mechanics, parallel universes, sub-atomic particles and the future of humanity. It is quite an adventure with many time-outs along the way, as we follow Mr. Tegmark's personal journey of job applications, rejected papers, close friendships and lost cars.

The book looks at two questions, which at first glance seem to have little in common: what is reality on the largest scale (what is the nature of the universe) and what is reality on the smallest scale (what are subatomic particles made of).

These are difficult questions because humans evolved to think about objects on a human scale. Mr. Tegmark uses clever examples, such as "Cosmic Legos" to help the reader establish appropriate metaphors. But, just when you think you understand the metaphors, he jumps into a discussion "quantum weirdness" and the "collapse of consensus" with glee and delight.

His favorite phrase is "crazy and counterintuitive," which applies not only to modern theories, but also applied to the 1600s, when astronomers started to realize that the Earth circled the sun and not the other way around. Mr. Tegmark notes that the crazy and counterintuitive sun-centric view became accepted when the empirical observations matched the predictions of elliptical orbits. It was the solid mathematics that provided the proof.

Mr. Tegmark goes onto argue that mathematics can explain ideas of parallel universes that come in different flavors. Fortunately for the reader, he provides a road map with different chapters directed to the science-curious reader, the hard-core reader of popular science, and the physicist. He also labels the status of each chapter on a scale from mainstream views to extremely controversial. The extremely controversial sections are where the reader is forced to come to grips with the most crazy and counterintuitive ideas.

Throughout the book, like a good teacher, Mr. Tegmark keeps you on track with periodic summaries called the bottom line, not that these are always definitive. Asking how will our universe end, he gives the humorous reply in the final chapter that it will probably end in a "Big Chill, Big Rip, Big Snap or with death by bubbles."

The book, however, is not just mathematics, physics and astronomy. On his roller coaster ride, Mr. Tegmark argues that advances in science are the result of individuals with their own curious history and personal quirks. Throughout, he talks about the debates, the personalities and other curious facts.

In the section on "The Joys of Getting Scooped," the author admits that he changed his birth name from Shapiro (his father's name) to Tegmark (his mother's name) because there were too many physicists named Shapiro and he wanted to stand out from the crowd when he coined the yet-to-be-found "Tegmark effect."

Along with his brother Per, they coined the word "Hurf!" to describe the moment you realize your important findings are not yours alone. The book contains plenty of moments of "hurf."

When you come down from the roller coaster, you realize you have been on quite a ride. Mr. Tegmark writes that "studying the foundations of physics isn't a recipe for glamour or fame: The best reason to do it is because you love it."

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